Geodesic
Nonlocal problem with dynamical boundary conditions for hyperbolic equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2017), pp. 18-25

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In this article, we consider a boundary-value problem with nonlocal dynamical conditions for hyperbolic equation. A feature of such conditions is the presence of both first and second order derivatives with respect to time-variable. Furthermore, boundary conditions are nonlocal to the extent that their representation is a relation between values of the derivatives on different parts of the boundary. The problem under consideration arise when we study vibration of a bar with damping and point masses. The existence and uniqueness of a generalized solution are proved. The proof is based on apriori estimates and Galerkin procedure.
Keywords: nonlocal problem, hyperbolic equation, generalized solution, second order derivatives, bar with damping, apriori estimates, Galerkin procedure.
Mots-clés : nonlocal dynamical conditions 
@article{VSGU_2017_3_a2,
     author = {A. V. Dyuzheva},
     title = {Nonlocal problem with dynamical boundary conditions for hyperbolic equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {18--25},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2017_3_a2/}
}
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A. V. Dyuzheva. Nonlocal problem with dynamical boundary conditions for hyperbolic equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2017), pp. 18-25. http://geodesic.mathdoc.fr/item/VSGU_2017_3_a2/